In the opinion of the inventors of the present invention, the type of compressor or pump known by the name of "sliding vane compressor or pump" is one of the most unintelligent and impractical devices ever put into practice in the field of fluid handling and measuring. The inventors of the present invention have invented a couple of different versions of the positive displacement fluid machine known as the "extending-retracting vane" or "folding-unfolding flap" meter-motor-pump as an alternative to the "sliding vane" compressor or pump, which inventions are described in U.S. Pat. Nos. 5,238,373 and 5,269,668, respectively. While those apparatus disclosed in the aforementioned U.S. Patents are suited to function as a flowmeter or pump pumping liquid media, they are ill suited to function as a compressor or pump pumping gaseous media as those apparatus have a large nonzero minimum separation angle between adjacent vanes occuring during rotation of the vane assembly. Such a large nonzero separation angle between adjacent vanes occurring in the returning phase of the vanes from the outlet port side to the inlet port side during the rotation of the vane assembly allows a significant portion of the fluid pumped from the inlet port side to the outlet port side to return to the inlet port side and, consequently, those devices described in the above-mentioned U.S. patents do not function efficiently and effectively as a compressor compressing a compressible fluid media and pumping it therethrough.